Heterogeneous Fixed Points with Application to Points-To Analysis

13 years 10 months ago

Download www.seas.upenn.edu

Many situations can be modeled as solutions of systems of simultaneous equations. If the functions of these equations monotonically increase in all bound variables, then the existence of extremal ﬁxed point solutions for the equations is guaranteed. Among all solutions, these ﬁxed points uniformly take least or greatest values for all bound variables. Hence, we call them homogeneous ﬁxed points. However, there are systems of equations whose functions monotonically increase in some variables and decrease in others. The existence of solutions of such equations cannot be guaranteed using classical ﬁxed point theory. In this paper, we deﬁne general conditions to guarantee the existence and computability of ﬁxed point solutions of such equations. In contrast to homogeneous ﬁxed points, these ﬁxed points take least values for some variables and greatest values for others. Hence, we call them heterogeneous ﬁxed points. We illustrate heterogeneous ﬁxed point theory through ...

Aditya Kanade, Uday P. Khedker, Amitabha Sanyal

Real-time Traffic